PS 366
Levels of Measurement
• How we classify / observe things
• Affects how they are described
• Affects what statistics we use to test hypotheses about relationships between things
Levels of Measurement
• Nominal– Things classified or categorized– No rank order– No scale
Race, gender, hair color,
Levels of Measurement
• Ordinal– Things classified, categorized– Things ordered, ranked– No set distance between categories– More of, less than
Satisfaction with democracy; prejudice; academic rank; party identification
Levels of Measurement
• Interval / ratio– Things measured on a continuous scale– Equal distance between units on scale– (if ratio) zero means zero
Age (years); GPA; income; education (years)
IQ; Celsius scale [zero = ??]
Levels of Measurement
• Some things (variables) can be measured at each level
• Example, Pain– Nominal– Ordinal– Numeric (interval)
Levels of Measurement
• Some things not clear cut
– Poverty– Freedom– Unemployment– Alienation
Levels of Measurement• Exercise: Create measures
of Education(how much)
– Nominal– Ordinal– Numeric (interval)
– As a question that can be asked on a survey
• Exercise: Create measures of Happiness
(how much)
– Nominal– Ordinal– Numeric
– As a question that can be asked on a survey
Levels of Measurement
• Why it matters?– If nominal, ordinal, interval:
– How do we describe• Central tendency?
• Variation?
• What graphics?
Nominal Data
• Simple percentages, proportions– Yes 45%, No 55%
• Most frequent occurrence (Mode)
• What is the meaning of the mean of gender?– 200 observations: M = 1, F = 2; mean = 1.5 ?
Example: General Social Survey
• Sex before marriage ok? permarsx
• Frequency distribution– Analyze -> Descriptive Stats ->frequency
– GSS Sex before marriage 1) always wrong, 2) almost always wrong, 3) sometimes wrong, 4) not at all wrong
Ordinal data frequency distribution
Ordinal Data
• How describe graphically?
• Bar charts (categories, but not range of variation)
Frequency of responses
Ordinal Data
– Very satisfied (1)12
– Satisfied (2)15
– Neither satisfied nor dissatisfied (3) 5
– Dissatisfied (4) 5
– Very dissatisfied (5) 3
• total40
Ordinal data
• Does it ‘behave’ like interval?
• Center: Mode
Interval Data
• Mean, median, mode – What is most representative observation
• Frequency distributions can be ‘normal’
Example: General Social Survey
• Analyze -> descriptives -> frequency
– Range 18 – 89 plus:
– What’s the distribution going to look like?
This is where Powerpoint crashed
Interval Data
• Standard deviation– how is what we observe
distributed around the central point
• Frequency distributions
Measuring Concepts
• But what is a variable?
• Something that varies– Influences something else; influenced by
something else
• Not a constant– Does not vary [Death, gravity, speed of
light ]
Measuring Concepts
• Measuring a variable =
• Quantifying a concept– turning a concept into something we can measure• Nominal, ordinal, interval
Measuring Concepts
• Variable = religion
• Type?
• Frequency?
• Intensity?
Measuring Concepts
• Religion:
– Type: Catholic, Baptist, None, Christian [self-identified]
– Frequency: How often attend religious services
– Intensity: Is Bible literally word of God? Do you believe Jesus is / is not son of God?
Measuring Concepts
• Religion:
– Type: nominal
– Frequency: Ordinal
– Intensity: Interval??? [religiosity?]
Measuring Concepts
• Candidate support
– Vote intention– Reported vote– “Feelings” [interval, intensity?]
Measuring Concepts• Candidate support
– Thermometer scores• Romney 50.4 (23%)• Pawlenty 48.4
(67)• Huntsman 47.9 (84)• Paul 46.3 (34)• Bachman 45.6 (55)• Santorum 43.9 (63)• Newt 42.7 (17)
value in parentheses = % unable to rank
• On a scale of 0-100, with 0 being cold, 50 being neutral, and 100 being warm, how would you rate your feelings rate the following candidates
• June 15, 2012
Reliability and Validity
• Reliability– Does the method of measuring produce the same
results when used by others
– Consider religion measures• Response to questions:
– what is your religion? __________________– how religious are you? _________________vs:– Check the label that applies to you [P, C, J, etc. ]– Closed response options [very, sort of, not, not at all]
Reliability and Validity
• Reliability– Does the method of measuring produce the same
results when used by others
– Consider Intelligence• Subjective judgment• Written narrative• IQ test
Reliability and Validity
• Validity– Construct Validity: does the measure really
measure the concept? [Religion & faith]
– Predictive Validity: does the measure predict what it should? [PID & voting]
– Content Validity: does the measure include things closely related to the concept?
Reliability and Validity
• Validity
– Face Validity: Does the measure correlate well with things related to the concept?
Reliability and Validity
• Validity
– IQ test measure; SAT score, GRE score
• What do they really measure?
• What do they predict?
• What should they predict if valid measures of ______
Reliability and Validity
• Validity?– Party Identification• Strong D• D• Ind, leans D• Ind• Ind, leans R• R• Strong R